For producing node, the superposing wave must travel in the opposite direction (x term must have opposite sign) and its displacement must be negative. Hence the correct option is y=-asin⁡(ωt+kx)
Moreover,
y=y₁+y₂=asin⁡(ωt-kx)-asin⁡(ωt+kx)
y=-2acosωtsinkx
At x=0, y = 0. That is a node is formed.